相关论文: Calm local optimality for nonconvex-nonconcave min…
In this paper, we study stochastic constrained minimax optimization problems with nonconvex-nonconcave structure, a central problem in modern machine learning, for which reliable and efficient algorithms remain largely unexplored due to its…
Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…
Recently, accelerated algorithms using the anchoring mechanism for minimax optimization and fixed-point problems have been proposed, and matching complexity lower bounds establish their optimality. In this work, we present the surprising…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
We revisit the smooth convex-concave bilinearly-coupled saddle-point problem of the form $\min_x\max_y f(x) + \langle y,\mathbf{B} x\rangle - g(y)$. In the highly specific case where each of the functions $f(x)$ and $g(y)$ is either affine…
Minimax optimization recently is widely applied in many machine learning tasks such as generative adversarial networks, robust learning and reinforcement learning. In the paper, we study a class of nonconvex-nonconcave minimax optimization…
We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator.…
We introduce the optimality question to the relaxation in multiple control problems described by Sobolev type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
In this paper, we focus on the decentralized composite optimization for convex functions. Because of advantages such as robust to the network and no communication bottle-neck in the central server, the decentralized optimization has…
This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…
Nonlinear embedding manifold learning methods provide invaluable visual insights into the structure of high-dimensional data. However, due to a complicated nonconvex objective function, these methods can easily get stuck in local minima and…
We consider the nonconvex minimization problem, with quartic objective function, that arises in the exact recovery of a configuration matrix $P\in \R^{nd}$ of $n$ points when a Euclidean distance matrix, \EDMp, is given with embedding…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
Minimax problems of the form $\min_x \max_y \Psi(x,y)$ have attracted increased interest largely due to advances in machine learning, in particular generative adversarial networks. These are typically trained using variants of stochastic…
Various optimal gradient-based algorithms have been developed for smooth nonconvex optimization. However, many nonconvex machine learning problems do not belong to the class of smooth functions and therefore the existing algorithms are…
This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
This paper is devoted to the study of approximate solutions for a multiobjective interval-valued optimization problem based on an interval order. We establish new existence theorems of approximate solutions for such a problem under some…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…